Measuring Your World Overview
The project Measuring your World underwent the explanation of the Pythagorean theorem and an overview of all the mathematical content that was prudent for our learning. For example, we started with Pythagorean and then went to understand formulas, the equation of a circle, the unit circle, the definition of sine, cosine and tangent, right-triangle trigonometry, area of polygons, area of a circle, and then volumes of many different shapes. For Pythagorean theorem we used the formula A^2 + B^2 = C^2 and we had to embody the true reason we use this formula to determine the exact length of the missing side., with no dimension on a side of a triangle. Then we consequently arrived at understanding how to reduce radicals. Then we transitioned to finding the distance between points on a coordinate plane. So we tried to understand the distance formula from finding the distance between two points and the formula is d = radical- (x1 - x2) ^2 + (y1 - y2) ^2. The Distance Formula is a "variant" of the Pythagorean Theorem that corresponds to past concepts I have learned. This formula is accurate because it accurately finds the true distance. We then switched to the equation of a circle and the formula is x2 + y2 = 4.
Overall, this accurately relates to the distance of a circle because we found exactly if the point is on the circle, or b. the point is inside the circle, or c. the point is outside the circle. The distance formula contrasting to the equation of a circle are also quite similar and are both a variant alike the Pythagorean Theorem. The circle is the set of points a fixed distance, radius, from a center point. This formula is consequently correct because the accuracy in the circles provided dimensions or information for the formula. For example, x−coordinate and the y−coordinate of the center, then the radius. Area of bases, finding area of all different types of shapes. We found shapes that are oblique, but that doesn't change the volume, so many other shapes we can change the volume of. We studied the definiton of cosine, tangent, and sine, then transitioning towards right- angle trig! Since the distance formula, like I mentioned is correlated to the Pythagorean Theorem, I saw similarities while learning sine, cosine and tangent. Ultimately making the understanding of formulas feasible and rememberable. Studying the area of a circle then volumes of many different shapes made the project complete because we studied were multiple concepts derived from and how they're proven.
Overall, this accurately relates to the distance of a circle because we found exactly if the point is on the circle, or b. the point is inside the circle, or c. the point is outside the circle. The distance formula contrasting to the equation of a circle are also quite similar and are both a variant alike the Pythagorean Theorem. The circle is the set of points a fixed distance, radius, from a center point. This formula is consequently correct because the accuracy in the circles provided dimensions or information for the formula. For example, x−coordinate and the y−coordinate of the center, then the radius. Area of bases, finding area of all different types of shapes. We found shapes that are oblique, but that doesn't change the volume, so many other shapes we can change the volume of. We studied the definiton of cosine, tangent, and sine, then transitioning towards right- angle trig! Since the distance formula, like I mentioned is correlated to the Pythagorean Theorem, I saw similarities while learning sine, cosine and tangent. Ultimately making the understanding of formulas feasible and rememberable. Studying the area of a circle then volumes of many different shapes made the project complete because we studied were multiple concepts derived from and how they're proven.
Design Your Own Project
Write Up
In this project, Measuring Your World, we had to explore measurement and the area of polygons/circles and then study volume in three dimensions. My group (Marissa and I) pondered about what we could measure to better understand and grow on the meaning of measurement, so by consequently trying to challenge and grow, my group of two calculated the volume of a Disney Mickey mouse pool. We were asked by the teacher to find the area or volume (perhaps both) of anything of your choice, then calculating the corresponding shapes, for example the polygons and circles areas. Our initial idea was to find the volume of an uniquely built pool with different dimensions that made it different compared to normal pools. We chose to do this because of the unique shapes it obtained. So we found a Disney themed pool that is in the shape of Mickey mouse’s head. The pools had three circles in total, we found the area of those shapes and that then led us to the volume of the pool.
The pool we chose had three circles in total and the depth for the two smaller circles in the pool is 2 feet, the bigger sized circle for (Mickey’s ears) is 5 feet. For Mickey’s head, referred to as the larger circle, has a radius of 6 and the two smaller pools are 3. So we found the area of the three circles that consumed the pool and then that led us to the volume. We utilized all of these dimensions and by determining the volume we used the formula V= π r2 h! We started small with our unique pool and found the total volume by finding the volume for the three separate circles. (Two smaller circles for the ears and the larger circle separate) So we plugged in the dimensions for Mickey's head and Mickey's ears into the formula for example V= π 62 (5) for the head and V= π 32 (2). Overall, the total volume of the whole Mickey pool is 678.59 cubic inches.
The pool we chose had three circles in total and the depth for the two smaller circles in the pool is 2 feet, the bigger sized circle for (Mickey’s ears) is 5 feet. For Mickey’s head, referred to as the larger circle, has a radius of 6 and the two smaller pools are 3. So we found the area of the three circles that consumed the pool and then that led us to the volume. We utilized all of these dimensions and by determining the volume we used the formula V= π r2 h! We started small with our unique pool and found the total volume by finding the volume for the three separate circles. (Two smaller circles for the ears and the larger circle separate) So we plugged in the dimensions for Mickey's head and Mickey's ears into the formula for example V= π 62 (5) for the head and V= π 32 (2). Overall, the total volume of the whole Mickey pool is 678.59 cubic inches.
Our successes were ultimately being proficient at our calculations and professional collaboration that made our process of our project smoother. No challenges occurred and that made our project idea feasible. In this project we have been becoming proficient at subjects such as the area of polygons/circles and then study volume in three dimensions. So, after spending class time learning more and more about these subjects, it made the overall project we made go smoother and advance our knowledge throughout the project even more. Overall, there are no changes we would make, except to next time extend into more challenging subjects. For example next time we would challenge ourselves to an even more complicated pool that had extra dimensions. Speaking for others and myself I believe one way to succeed at this project is to start small and really utilize that habit of a mathematician. Without taking apart and putting back together your idea, you're going to feel bombarded by so many dimensions all together and not know how to solve for your idea.
Reflection
Math 2
When we were introduced different concepts/topics of math such as concept's of measurement and formal and informal proofs of measurement formulas, I thought that even though we covered concepts I had skimmed over previously, we covered it in a different/ new way. So this ultimately gave me a whole new understanding for me on measurement, especially learning about the formulas we use and why we use them.
Overall, I accomplished a whole new understanding of how measurement can be applied to better understand our world and different objects measurements. By some concepts being talked about in a new way, done differently, it definitely helped me because of the also similar correlation between formulas. These correlation's did connect formulas and these concept's together into a larger meaning as well. After finding the area of bases, finding area of all different types of shapes, we found shapes that are oblique, but that doesn't change the volume, so there are many other shapes we can change the volume of. We studied one dimension with the Pythagorean Theorem and distance, then moved into two dimensions with right triangle trigonometry and the area of polygons and circles. Then overall we concluded with studying volume in three dimensions. One important concept I took away from this project while finding the volume and surface area of 3D objects was if you really articulate and understand the formulas we learn as I go, it will help me understand what's going on in future math studies. Helping me recognize the correlation between formulas, for example the Pythagorean Theorem and distance.
Overall, I accomplished a whole new understanding of how measurement can be applied to better understand our world and different objects measurements. By some concepts being talked about in a new way, done differently, it definitely helped me because of the also similar correlation between formulas. These correlation's did connect formulas and these concept's together into a larger meaning as well. After finding the area of bases, finding area of all different types of shapes, we found shapes that are oblique, but that doesn't change the volume, so there are many other shapes we can change the volume of. We studied one dimension with the Pythagorean Theorem and distance, then moved into two dimensions with right triangle trigonometry and the area of polygons and circles. Then overall we concluded with studying volume in three dimensions. One important concept I took away from this project while finding the volume and surface area of 3D objects was if you really articulate and understand the formulas we learn as I go, it will help me understand what's going on in future math studies. Helping me recognize the correlation between formulas, for example the Pythagorean Theorem and distance.